Related papers: Efficient Bayesian estimation of a non-Markovian L…
Langevin models are frequently used to model various stochastic processes in different fields of natural and social sciences. They are adapted to measured data by estimation techniques such as maximum likelihood estimation, Markov chain…
Modeling non-Markovian time series is a recent topic of research in many fields such as climate modeling, biophysics, molecular dynamics, or finance. The generalized Langevin equation (GLE), given naturally by the Mori-Zwanzig projection…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…
Recent pioneering experiments on non-Markovian dynamics done e.g. for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still…
This paper aims to investigate the non-Markovian dynamics. The governing equations are derived for the probability density functions (PDFs) of non-Markovian stochastic responses to Langevin equation excited by combined fractional Gaussian…
Dynamics of non-Markovian systems is a classic problem yet it attracts an everlasting activity in physics and beyond. A powerful tool for modeling such setups is the Generalized Langevin Equation, however, its analysis typically poses a…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the…
Motivated by decentralized approaches to machine learning, we propose a collaborative Bayesian learning algorithm taking the form of decentralized Langevin dynamics in a non-convex setting. Our analysis show that the initial KL-divergence…
One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
Analysis of non-Markovian systems and memory induced phenomena poses an everlasting challenge for physics. As a paradigmatic example we consider a classical Brownian particle of mass $M$ subjected to an external force and exposed to…
Every quantum system is coupled to an environment. Such system-environment interaction leads to temporal correlation between quantum operations at different times, resulting in non-Markovian noise. In principle, a full characterisation of…
Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are…
We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is…